In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

The robust nonlinear adaptive filtering problem based on Volterra model is researched when the input and output observation data are both corrupted by noise in this paper. On the basis of minimizing Volterra total mean square error (VTMSE), a robust total least mean square adaptive filtering algorithm for nonlinear Volterra filter is proposed. The performance analysis demonstrates that the robu...

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...

We propose a new class of mapping-based nonlinear quadratic Volterra filters for image enhancement. The input signal is mapped prior to filtering by a memoryless one-to-one nonlinear mapping function. The mapping function can be described by any arbitrary function and implemented by a simple look-up table. If necessary, an inverse mapping function is applied after filtering. Using this general ...

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

The starting point of this paper is the definition of a nonlinear model of the read out process in high density optical discs. Under high density condition, the signal read out is not a linear process, and suffers also from cross talk. To cope with these problems, the identification of a suitable nonlinear model is required. A physical model based on the optical scalar theory is used to identif...

Reliable channel modeling becomes an important measure in performance evaluation on various data detection algorithms. For this reason, correct and accurate modeling is required. This paper presents a nonlinear modeling of Super-RENS (Super-Resolution Near Field Structure) read-out signal using the second-order Volterra and neural network models. The experiment results verified the possibility ...

We survey continuous and discrete regularization methods for first-kind Volterra problems with continuous kernels. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on computation of the Volterra adjoint operator, an anticipatory operator. In this survey we pay special attention to partic...

• TOP OF ARTICLE • INPUT-OUTPUT SYSTEM REPRESENTATION • NONLINEAR DIFFERENTIAL ALGEBRAIC REPRESENTATION • VOLTERRA REPRESENTATION • STATE-SPACE REPRESENTATION • BILINEAR REPRESENTATION • NARMA REPRESENTATION • FUZZY-LOGIC NONLINEAR REPRESENTATION • NONLINEAR REPRESENTATION USING NEURAL NETWORKS • MODEL-FREE REPRESENTATION • FEATURES OF NONLINEAR REPRESENTATIONS • EXAMPLE • CONCLUDING REMARKS • ...

Adaptive nonlinear filtering plays an important role in audio signal processing and echo control. In this contribution a nonlinear system identification method is proposed. The setup is built using adaptive Volterra filters of second and third order with the same memory length. The adaptation is achieved using a Normalized Least Mean Square algorithm with a proper selected stepsize parameter fo...